The R-index: A universal metric for evaluating OAM content and mode purity in optical fields

TL;DR

The paper introduces the R-index, a universal metric that quantifies the intrinsic orbital angular momentum and purity of structured optical fields, enabling better comparison and optimization of optical beams for various applications.

Contribution

It presents the R-index as a novel, comprehensive measure for evaluating OAM content and mode purity in complex optical fields, unifying characterization methods.

Findings

The R-index accurately quantifies total OAM in multi-vortex fields.

It assesses the purity and fidelity of OAM generation.

The metric enables comparison across diverse optical beam profiles.

Abstract

Despite its pivotal role in optical manipulation, high-capacity communications, and quantum information, a general measure of orbital angular momentum (OAM) in structured light remains elusive. In optical fields, where multiple vortices coexist, the local nature of vortex OAM and the absence of a common rotation axis make the total OAM of the field difficult to quantify. Here, we introduce the R-index, a metric that captures the intrinsic OAM content of any structured optical field, from pure Laguerre-Gaussian modes to arbitrary multi-vortex superpositions. Not only does this metric quantify the total OAM, it also assesses field purity, providing insight into the fidelity and robustness of the OAM generation. By unifying OAM characterization into a single figure of merit, the R-index enables direct comparison across diverse beam profiles and facilitates the identification of optimal configurations for both foundational studies and applied technologies.